There are GPS devices used to detect the current position of a vehicle and to show the user a route to a destination. A GPS device installed in a vehicle receives a carrier wave modulated by a pseudorandom code from a GPS satellite and calculates the distance from the GPS satellite by multiplying light velocity and propagation time of the carrier wave obtained in the demodulation process. The position of a vehicle on the Earth is determined in a three-dimensional space defined by latitude, longitude, and altitude (hereafter, these are simply called coordinates). Therefore, a GPS device receives times of origin from three GPS satellites and obtains the coordinates of the vehicle by calculating an intersection point of spheres each having a radius that is the distance between the vehicle and the corresponding one of the three GPS satellites. Meanwhile, although a GPS satellite is equipped with an extremely high-precision clock, a clock in a vehicle is less precise. Therefore, the obtained propagation time necessarily includes an error and the calculated distance from the GPS satellite becomes inaccurate. To solve or reduce this problem, a GPS device normally uses a fourth GPS satellite to correct a time error and thereby to accurately detect the position of a vehicle.
However, in the case of a GPS device installed in a mobile body such as a vehicle, the GPS device may not always be able to receive radio signals carrying times of origin from all four GPS satellites. In an in-vehicle positioning system, the current position of a vehicle is estimated by autonomous navigation and/or a map matching method when radio signals from GPS satellites are not available. However, the accuracy of the estimated position decreases if GPS satellite signals are not available for a long time.
Patent document 1 discloses a method that enables detection of the position of a vehicle even when a radio signal is only available from one GPS satellite. In the disclosed method, a circle supposedly including the current position of a vehicle is calculated based on a radio signal from a GPS satellite. Also, a current travel direction of the vehicle is obtained by updating the direction of the vehicle with, for example, a gyro sensor. The current position of the vehicle is obtained by calculating an intersection point of the circle and the current travel direction.
[Patent document 1] Japanese Patent Application Publication No. 8-75479